Joel E. Cohen, Abby Rockefeller Mauze Professor of Populations at The Rockefeller University and Professor of Populations at the Earth Institute of Columbia University, is an eminent mathematical biologist who, as his titles suggest, is a leading expert in demographics. He is also a key contributor to our book (Demografiction, p. 122).
In a recent note Cohen compliments our own David Shugarts for his insight that Dan Brown’s math is fundamentally flawed. Brown calculates that “Zobrist’s virus” will have an impact on only one third of the world’s population (p. 202). Shugarts observes that Brown is implicitly assuming that the one third of men who are sterilized will mate only with the one third of women who are sterilized. Shugarts points out that if the sterilized men and women “were to marry exclusively unaffected partners, that would result in two thirds of couples being infertile.”
Professor Cohen then goes on to add an additional thought “for those of us who love probability theory and combinatorics:”
If the sterilized one-third of the population were mated randomly (which would be plausible if they did not know that they were sterilized), then the fraction of couples in the population who were sterilized would be 5/9 (assuming, contrary to fact, that each individual belonged to one and only one couple). You can derive 5/9 as 1/3 + 1/3 – 1/9 (where the last term, 1/9, removes the double counting of couples in which both partners are sterilized) or as (1/3)(2/3) + (1/3)(2/3) + 1/9 (where the first term counts the fraction of sterilized women who are coupled to non-sterilized men, the second term counts the fraction of sterilized men who are coupled to non-sterilized women, and the third term counts the fraction of sterilized women who are coupled to sterilized men). Fun and games. The point of these three different calculations (1/3, 2/3, 5/9) is that the impact of sterilizing one third of the population randomly depends on people’s behavior and whether they know they are sterilized.
We thank Professor Cohen for his observation and welcome the ongoing conversation about our book and the issues it raises.